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{"type":"item.completed","item":{"id":"item_2","type":"agent_message","text":"```python\nimport numpy as np\nimport scipy.linalg as la\nfrom threadpoolctl import threadpool_limits\nnp.set_printoptions(precision=4, suppress=True, linewidth=180)\n\ndef svd(a):\n    return la.svd(a, full_matrices=False, lapack_driver=\"gesvd\")\ndef whiten(g):\n    e,u=la.eigh(g)\n    return (u/np.sqrt(np.maximum(e, e[-1]*1e-6)))@u.T\n\nwith threadpool_limits(limits=2):\n    g=np.asarray(W[\"ln1_w.0\"],dtype=float)\n    bs=[]\n    for j in range(6):\n        s=slice(j*64,(j+1)*64)\n        bs.append((np.asarray(W[\"W_o.0\"][:,s],dtype=float)@np.asarray(W[\"W_v.0\"][s],dtype=float))*g)\n    u,s,vt=svd(np.hstack([bs[j] for j in (0,1,4,5)]))\n    R=u[:,:3]\n    print(\"COMMON L0 BROAD-HEAD WRITE SUBSPACE: singular values\",s[:12])\n    print(\"Fraction of each head's OV energy in that 3D write subspace:\")\n    print([round(la.norm(R.T@b)**2/la.norm(b)**2,4) for b in bs])\n    print(\"Top coordinates of its three orthonormal directions:\")\n    for z in range(3):\n        ix=np.argsort(-abs(R[:,z]))[:8]\n        print(z, list(zip(ix.tolist(),np.round(R[ix,z],4).tolist())))\n\n    print(\"\\nLATER QK FRACTION USING COMMON 3D WRITE SUBSPACE\")\n    print(\"query-side, key-side, both-sides; bias-derived key coefficient fraction in this subspace\")\n    for l in range(1,4):\n        g1=np.asarray(W[f\"ln1_w.{l}\"],dtype=float)\n        b1=np.asarray(W[f\"ln1_b.{l}\"],dtype=float)\n        for j in range(6):\n            sl=slice(64*j,64*j+64)\n            q=np.asarray(W[f\"W_q.{l}\"][sl],dtype=float)\n            k=np.asarray(W[f\"W_k.{l}\"][sl],dtype=float)\n            raw=q.T@k/8\n            a=(g1[:,None]*raw)*g1\n            keycoef=(b1@raw)*g1\n            vals=[la.norm(R.T@a)**2/la.norm(a)**2,\n                  la.norm(a@R)**2/la.norm(a)**2,\n                  la.norm(R.T@a@R)**2/la.norm(a)**2,\n                  la.norm(keycoef@R)**2/(la.norm(keycoef)**2+1e-30)]\n            print(f\"L{l}H{j}\",np.round(vals,4))\n            if l==1:\n                print(\"3D coefficient matrix\",np.round(R.T@a@R,4).tolist(),\n                      \"key-linear coefficients\",np.round(keycoef@R,4).tolist())\n\n    print(\"\\nL0H2 RAW OV SINGULAR VALUES\")\n    braw=np.asarray(W[\"W_o.0\"][:,128:192],dtype=float)@np.asarray(W[\"W_v.0\"][128:192],dtype=float)\n    print(svd(braw)[1][:64])\n\n    print(\"\\nMLP ROW CROSS-COVARIANCES IN L0H2 READ SUBSPACES\")\n    print(\"X = M T; Y = M B T. This compares weight-row geometry, without evaluating any neuron.\")\n    M=np.asarray(W[\"W_fc.0\"],dtype=float)*W[\"ln2_w.0\"]\n    for gain in (False,True):\n        B=bs[2] if gain else braw\n        _,_,vt=svd(B)\n        for rank in (16,24,28,40):\n            T=vt[:rank].T\n            X=M@T\n            Y=M@B@T\n            X=X-X.mean(axis=0)\n            Y=Y-Y.mean(axis=0)\n            X/=la.norm(X)\n            Y/=la.norm(Y)\n            G=(X.T@X+Y.T@Y)/2\n            iw=whiten(G)\n            C=iw@((X.T@Y+Y.T@X)/2)@iw\n            e=la.eigvalsh(C)\n            print(f\"gain={gain}, rank={rank}: Frobenius_cos={np.sum(X*Y):.4f}, \"\n                  f\"sym_generalized_eigs={np.round(e,3)}\")\n```"}}
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